It just doesn't work that way Martin. If they are not at the specialist school from the word go they loose critical time in that speciality, as you well know.
Not true. Children start to learn musical instruments at different times and reach various standards at different times. Very often a school will have a peripatetic teacher, for instruction in a particular instrument, whose skills will suffice to a certain level. At some stage, dependent on the skills of that teacher, the peripatetic teacher may say that a pupil has attained such a high standard that they have reached the limit of what that teacher can teach them, and this can happen at various ages. So it's at that point that the pupil and her parents, taking advice from the school, might consider transfer to a specialist school where a more intense programme under the instruction of a more highly qualified teacher can be embarked upon.
So, are you suggesting that a pupil who shows remarkable talent in playing the flute, say, at the age of 14 is necessarily going to develop to the same level of a child who was at that level at, say, 8? The child found to be a prodigy at 14 will have lots of other things to think about in their life - GCSE's in general, friends, sex and sexuality, ...
They're not starting from the same starting point.
Like Andrew, I believe that you are proposing a Utopian idea that is largely unworkable in real life without a completely different approach to the importance of exams and qualifications in society. Only then, when exams become largely obsolete, and professional qualifications are only achieved 'in post', would any of your ideas even have a hint of a chance of succeeding.